Parallel kinematic structure for spatial positioning devices and method of initializing same

ABSTRACT

A coordinate measuring machine (CMM), including three spherical base joints, a device for maintaining the base joints in a fixed spaced relation, and six actuator assemblies each having a variable length. Each of the base joints has a first end of two of the six actuator assemblies connected therewith, respectively. A center pole is provided having a first spherical joint connected to a first end thereof and a second spherical joint connected to a second end thereof. A second end of a first one of each of the two actuator assemblies connected to each of the base joints is connected to the first spherical joint of the center pole, and a second end of a second one of each of the two actuator assemblies connected to each of the base joints is connected to the second spherical joint of the center pole, in a manner which forms a hexahedron. The coordinate measuring machine further includes a probe mounted at one end of the center pole and a laser interferometer for determining a change in length of each of the six actuator assemblies upon movement of the probe. A method for initializing the CMM and an improved universal joint having a reference sphere therein for use in the CMM are also disclosed.

BACKGROUND OF THE INVENTION

Reference is hereby made to provisional patent application Ser. No.60/004,253 filed Sep. 25, 1995, the benefit of the filing date of whichis claimed herein.

1. Field of the Invention

The present invention relates to a kinematic structure for spatialpositioning devices and, more particularly, to a hexahedron coordinatemeasuring machine (CMM), a method of initializing same and an improveduniversal joint for use in connection with coordinate measuringmachines.

2. State of the Art

The present invention concerns the application of a novel parallelkinematic system to coordinate measuring machines. Coordinate measuringmachines (CMMs) are widely used in industry for dimensional inspectionof manufactured parts. CMMs normally consist of several functionalcomponents. A table is provided where the parts to be measured can befixtured. A probe senses the edges and surfaces of the features to bemeasured on the part. A kinematic structure provides relative motionbetween the part and the probe and allows the probe to be moved to theproper locations on the part. A position sensing system reports thespatial coordinates of the probe at each measured location. Thesecoordinate locations are processed by measurement software to determinethe locations, dimensions and geometry of the part features.

The vast majority of CMMs use a kinematic structure consisting of aserial chain of three prismatic joints arranged to be mutuallyperpendicular, thus providing a physical embodiment of a Cartesiancoordinate system. The position sensing system is then provided bydisplacement sensors (scales) along each slide (coordinate axis). Avariety of probes may be carried by these machines, includingtouch-trigger, capacitance and optical devices. Since this kinematicstructure does not allow the probe to be oriented with respect to theworkpiece, some probe manufacturers provide motorized or manual indexingcapability. This allows the probe to be oriented as needed with respectto particular features on the part.

The measurement accuracy of these types of CMMs is greatly affected bythe precision with which the individual components are manufactured andassembled. Individual axis slides will not be perfectly straight ororthogonal to the others. Elastic deformations of the structuralcomponents compound this problem. For this reason, CMM components aretypically designed to be as stiff as possible which often results inlarge, heavy machines.

Significant improvements in CMM accuracy can be achieved if thepositioning errors of the machine are premeasured and compensationsoftware is used to process the output data. This approach is currentlyin widespread use by CMM manufactures and allows the accuracy of themachines to be improved at a reasonable cost.

Despite the significant improvements in CMM performance over the pastdecade, several factors still limit CMM accuracy, speed and economicutility. Thermal variations in the CMM environment cause expansion andcontraction of the individual components. This, in turn, distorts theelements of the kinematic structure, causing positioning errors of theprobe tip. CMM manufacturers routinely supply algorithms to compensatefor thermal expansion and contraction of the machine scales. Specialsoftware uses temperature sensors on the individual scales to modify thescale output based on the coefficient of thermal expansion of the scalematerial. If all parts of the machine are at the same temperature, thenthis approach is satisfactory. However, in an environment where thetemperatures change or there are heat sources in the vicinity of theCMM, thermal gradients will occur in the machine structure. Thesegradients will distort the machine geometry in a manner which cannot becorrected by currently available methods, thus causing a seriousdegradation in the accuracy of the machine. For this reason, virtuallyall CMMs used for moderate- to high-precision inspection are housed inspecially constructed rooms with carefully controlled environments. Thisrequirement substantially increases the cost of CMM installation andusage. Furthermore, it forces the CMMs to be somewhat remote from themanufacturing floor, causing a disruption in the production flow anddecreasing the utility of the machines.

A second limitation on CMMs performance is related to their dynamicperformance. When large numbers of parts are being inspected, theinspection time becomes critical. For any given part geometry andfeatures to be inspected, the inspection time is largely determined bythe speed with which the CMM can move the probe tip from point to point.However, high speeds and accelerations are difficult to obtain when thekinematic structure is made up of large elements with significant mass.Furthermore, these machines typically possess very small damping, due inlarge part to the air-bearing slides used to reduce friction andhysteresis in the axis motions. The result is that significantvibrational deflections of the machine structure may occur when themachine speeds and accelerations are high. These deflections also causea loss of accuracy and repeatability of the machines.

The CMM kinematic structure of the present invention is based onarranging the actuators in a parallel, as opposed to a serial, fashion.The most well-known example of a parallel manipulator is the StewartPlatform. Recently, machine tools based on variations of thisarchitecture have been introduced. Parallel mechanisms of this type havesix prismatic actuators connecting the moving body (platform) to thefixed body (base). Each of these actuators is connected to each of thebodies by spherical joints. By proper control of the individual actuatorlengths, the position and orientation of the platform can be controlledin all six spatial degrees of freedom.

For fixed geometries of the base and platform, it is possible toformulate analytical expressions which give the position and orientationof the platform with respect to the base in terms of the lengths of thesix actuators and the coordinates of the centers of each of thespherical joints on the base and platform. These expressions take theform of high order polynomials (up to 40th order), each root of whichcorresponds to a possible position and orientation.

Parallel mechanisms of this type are generally thought to possessoutstanding rigidity relative to their weight. However, the reachablework volume tends to be small compared to the overall size of themachine. The first machine tools based on this architecture are just nowbecoming commercially available. More research, study and experiencewill be needed to assess their success or failure.

The design of a machine to perform precision dimensional measurementrequires several basic tasks to be completed. First, a length reference(metric) and a means of transferring or establishing that metric in theworkspace of the machine must be established. Second, a referencecoordinate system whose origin and geometry are known must beestablished. Third, the generation of repeatable motions of the proberelative to the workpiece in a manner such that these motions can bemeasured relative to the reference coordinate system using the metricmust be enabled. Fourth, the characteristics of the probe must be knownsince it links the measuring machine to the part being measured. Theaccuracy of the machine will depend on the degree of success inaccomplishing each of these tasks.

A number of design principles which experience has shown will lead toaccomplishing these tasks in an optimal manner are as follows:

1. Isolation of the device, which means that the disturbing effects ofenvironmental factors such as temperature, humidity, vibration, etc., onthe accuracy of the instrument should be minimized. Design strategiesinclude control of the environment, decoupling from the environment anddesign of the instrument so that its response to these disturbances isminimal. Current generation CMMs typically make use of the firststrategy, i.e., control of the environment.

2. Whenever one body is mounted on another, the connection between thetwo should be designed to provide the minimum level of constraintnecessary. Over-constraint or redundant constraints will cause thebodies to distort in a manner which is difficult or impossible topredict. The principle of exact mechanical constraint is termed"kinematic mounting."

3. The alignment principle, or Abbe principle, is also known as "thefirst principle of mechanical design and dimensional metrology."Satisfaction of the alignment principle requires that the measurementaxis of the displacement measuring system be placed so that its line ofaction passes through the point whose displacement is to be measured,i.e., the probe tip. If this is not possible, i.e., there exists anoffset between the point of interest and the measurement axis, then theangular motions of the carriage must be measured and the displacement ofthe point must be calculated based on their effect. It is difficult orimpossible to design a Cartesian mechanism so that the displacementmeasuring devices on the individual axes satisfy the Abbe principle.

4. If possible, the metrology system should be separate from thestructural loop which carries the forces due to the weights and inertiasof the moving elements of the machine so that deformations of thestructural members under these loads do not induce metrology errors.Because of the added expense, most current generation CMMs do not use aseparate metrology frame.

The design principles given above can be used to formulate a set ofdesign requirements necessary to obtain accuracy in Cartesian CMMs witha serial kinematic structure, as follows:

1. The guideways should be as straight as possible. This is necessarysince it is impossible to satisfy the Abbe alignment principle for allthree axes. Therefore, extremely straight guideways are needed toprevent the moving bodies from rotating and causing displacement errors.It has been postulated that, using conventional practice (i.e.,manufacturable at a reasonable cost), straightnesses of 1 μm/m areachievable.

2. The machine elements should be very stiff. Creation of very straightguideways is not sufficient if they sag under the weight of the movingbodies which they must support. This leads inevitably to large, heavystructures; i.e., qualities which are detrimental to the dynamiccapabilities of the machine.

3. The guideways must be aligned very precisely. The guidewaysessentially form the reference coordinate system for displacementmeasurements in many machines. Therefore, if they are not arranged to beperfectly orthogonal to each other, measurement errors will result.

4. A reliable and accurate displacement measuring system is required formeasuring displacements of the individual slides along the guideways.

It is interesting to compare the design requirements for accuracy inparallel kinematic structures with those for serial kinematicstructures. In parallel structures, the position and orientation of themoving body are obtained from the solution of a set of geometricrelationships. The inputs to these relationships are the geometry of thebase and platform (i.e., the coordinates of the centers of the sphericaljoints), and the absolute lengths (distances between joint centers) ofthe six actuators. Therefore, in order to achieve accuracy in a parallelmechanism, one needs to realize the following requirements:

1. The spherical joints should produce perfect spherical motion. Theactuators must rotate about fixed points on the base and platform.

2. The absolute distance between the centers of corresponding sphericaljoints on the base and platform must be measured with a high degree ofaccuracy. This is in distinct contrast to serial mechanisms where onlythe displacement along each axis is needed. In general, displacementmeasuring devices will be used to measure the changes in length of theindividual legs. Therefore, a system for determining the initial lengthsmust be developed since it will be impossible to bring the joint centerson the base and platform into coincidence to make the leg length equalzero, thus providing an absolute reference for the displacementmeasuring system.

3. The geometry of the base and platform must be stable and known tohigh accuracy. Since the position of the probe is dependent on thecoordinates of the joint centers on the base and platform, it followsthat any deformations of these bodies will cause errors in thatposition. Therefore, the base and platform should be rigid and thermallystable. This is a difficult design requirement since the base isphysically large for machines with usefully large work volumes.Therefore, the joint centers are physically separated by a significanteffective length of material. Any temperature changes in that materialmay result in significant changes of the geometry and lead to largepositioning errors. This requirement can be relaxed if it is possible tomonitor the actual positions of the joint centers while the instrumentis in use.

The first two requirements are descriptions of the functionalcapabilities of the laser ball bar (LBB), described in U.S. Pat. No.5,428,446 issued Jun. 27, 1995. The LBB is essentially an extensibleprismatic strut with spherical joints on the ends. These sphericaljoints are formed by precision spheres riding in magnetic sockets. Themagnetic sockets maintain three-point contact with the spheres inconformance with the principle of kinematic mounting. Spheres with formaccuracies better than 5 μin (125 nm) are readily and inexpensivelyobtainable. When combined with the magnetic sockets, the resulting jointproduces spherical motion to within 2.5 μin (62.5 nm).

A laser interferometer is used with the LBB to measure displacements orlength changes of the LBB. The initialization fixture allows the outputof the interferometer to be initialized to the absolute distance betweenthe centers of the spherical joints. In fact, the trilaterationprocedure used by the LBB to measure the spatial coordinates of the toolcan be viewed as a degenerate form of Stewart platform mechanism. If theplatform of such a mechanism shrinks to a single point so that all ofthe joint centers on it become coincident, then a tetrahedron is formed.The LBB sequentially measures the lengths of the sides of thistetrahedron to obtain the spatial coordinates of the apex. Thus, the LBBnaturally satisfies two of the design requirements for accurate parallelmechanisms.

Thus, a need exists for an improved coordinate measuring machine (CMM)that satisfies the requirements set forth above, but does not have thedisadvantages of known CMMs. There is a further need for a platform-typedevice with high positional accuracy, which device uses the LBB as abuilding block for creating the device.

SUMMARY OF THE INVENTION

It is, therefore, a primary object of the present invention to providean improved coordinate measuring machine for dimensional inspection ofmanufactured parts, or the like.

A further object of the present invention is to provide an improvedcoordinate measuring machine having actuators arranged in parallel andsimilar in structure to the actuators used in the laser ball bar (LBB)disclosed in U.S. Pat. No. 5,428,446.

Another object of the instant invention is to provide an improvedcoordinate measuring machine which is self-initializing.

Yet another object of the instant invention is to provide an improvedcoordinate measuring machine which is insensitive to changes inenvironmental conditions and does not require a temperature controlledenvironment for accurate operation.

An additional object of the invention is to provide an improvedcoordinate measuring machine that is operable to continuouslyself-initialize so as to automatically compensate for thermally inducedchanges in the parts comprising the machine.

A more specific object of the instant invention is to provide animproved coordinate measuring machine which does not require the use oflarge, heavy parts, and enables the probe thereon to be moved relativelyquickly between coordinates.

Still another object of the invention is to provide an improvedcoordinate measuring machine which has a relatively large locus ofattainable positions.

A further object of the invention is to provide a method of initializinga hexahedron coordinate measuring machine.

Yet another object of the invention is to provide an improved universaljoint for use in parallel kinematic structures, which joint helps toassure that true spherical motion is achieved in the joints duringoperation of the machine.

Still another object of the invention is to provide an improvedcoordinate measuring machine having improved dynamic performance due tolow mass of the moving elements and the insensitivity of the probeposition to bending of the actuators.

A still further object of the invention is to provide an improvedcoordinate measuring machine which enables reduced operational andinspection costs as compared to known devices.

These and other objects and advantages are achieved by the presentinvention, which provides a coordinate measuring machine, includingthree spherical base joints, means for maintaining the base joints in afixed spaced relation, and six actuator assemblies each having avariable length. Each of the base joints has a first end of two of thesix actuator assemblies connected therewith, respectively. A center poleis provided having a first spherical joint connected to a first endthereof and a second spherical joint connected to a second end thereof.A second end of a first one of each of the two actuator assembliesconnected to each of the base joints is connected to the first sphericaljoint of the center pole, and a second end of a second one of each ofthe two actuator assemblies connected to each of the base joints isconnected to the second spherical joint of the center pole, in a mannerwhich forms a hexahedron. The coordinate measuring machine furtherincludes a probe mounted at one end of the center pole and means fordetermining a change in length of each of the six actuator assembliesupon movement of the probe, such as, for example, a laserinterferometer.

In accordance with another aspect of the invention, the base joints andfirst and second spherical joints are spheres, and the first and secondends of the actuator assemblies are magnetic sockets which enableconnection with the respective spheres by a magnetic force.

In accordance with another aspect of the invention, the base joints andthe first and second spherical joints are universal joints, wherein eachjoint includes a stationary reference sphere mounted at a center pointthereof, and the machine further includes means for using the referencesphere to enable compensation for any non-spherical motion by theuniversal joints during movement of the probe.

In accordance with yet another aspect of the invention, a method isprovided for initializing the hexahedron coordinate measuring machine,including the steps of displacing the center pole a plurality of times,obtaining information on a change in the length of each actuatorassembly for each displacement, and using the information obtained and aleast square algorithm to determine the initial length of each leg and adistance between each of the base joints, thereby initializing themachine.

In accordance with a further aspect of the invention, a method and meansare disclosed for continuously self-initializing the machine, so thatthe machine becomes insensitive to environmental conditions.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and advantages of the subject invention will becomeapparent from a study of the following specification when viewed inlight of the accompanying drawings, in which:

FIG. 1 shows an elevational view of a preferred embodiment of thecoordinate measuring machine (CMM) of the instant invention;

FIG. 2 shows the locus of attainable positions for the first and secondspherical joints on the center pole of the coordinate measuring machine(CMM) of FIG. 1;

FIG. 3 shows an enlarged view of the second or lower spherical joint onthe center pole, the three magnetic sockets connected therewith and theprobe of FIG. 1;

FIG. 4 shows a diagrammatic view of the operation of the laserinterferometer used with the coordinate measuring machine (CMM) of FIG.1; and

FIG. 5 shows a perspective view of a preferred embodiment of an improveduniversal joint for use on the coordinate measuring machine (CMM) ofFIG. 1.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Referring now to the drawings, wherein like reference numerals designatesimilar parts throughout the various views, and more particularly toFIG. 1, there is shown a preferred embodiment of the coordinatemeasuring machine (CMM) 10 of the instant invention. The CMM 10 includesa granite baseplate 12, or other rigid base plate, supporting threeposts or legs 14. A ring member 16 is kinematically mounted to the posts14, and three spherical base joints 18 are attached to the insidesurface of the ring 16. Six actuator assemblies, preferably in the formof telescoping rods or legs, are provided, wherein two actuatorassemblies 20 and 22 have a first end connected with each of thespherical base joints 18, respectively. The actuator assemblies 20 and22 are preferably similar to the type shown in U.S. Pat. No. 5,428,446,known as the laser ball bar (LBB), which patent is hereby incorporatedherein by reference. The LBB provides a ball bar gage that integrates anlaser interferometer with a telescoping ball bar. As will be explainedin more detail below, the laser interferometer enables information onthe changes in length of each of the actuator assemblies 20 and 22 to bemeasured. While actuators in the form of LBBs are preferred, any type ofsuitable actuators and means for measuring changes in length thereof canbe used in accordance with the instant invention. In accordance with theinvention, the actuator assemblies may be either passive or activeactuator assemblies. In other words, any type of variable length linearmotion device may be used to define the actuator assemblies.

The CMM further includes a center pole 24 having a spherical joint 26and 28, respectively, at each end thereof. One actuator 20 of the twoactuators 20 and 22 connected to each base joint 18 has a second endconnected to the upper spherical joint 26 on the center pole 24. Theother actuator 22 connected to each base joint has a second endconnected to the lower spherical joint 28 on the center pole 24. Thus,the upper and lower spherical joints on the center pole 24 each carrythe ends of three actuators, one from each base socket 18. In thismanner, a hexahedron is formed consisting of two tetrahedra with acommon base.

The CMM 10 further includes a probe 30 attached to the lower sphericaljoint 28 of the center pole 24. The probe is preferably a touch-triggertype probe, but a capacitance or optical probe or any other suitableprobe that senses contact can be used. The probe 30 is mounted such thatthe center of its tip 64 is collinear with the centers of the top andbottom spherical joints 26 and 28.

The workspace of the CMM 10 is complex in shape. Visualization of theworkspace geometry is complicated by the ability to position the tip 64of the probe 30 at a given location, but with an arbitrary orientation.FIG. 2 shows the locus 32 of attainable positions for the upper andlower spherical joints 26 and 28 of the center pole 24. In oneembodiment, that machine was sized to provide a workspace which wouldminimally encompass a cylinder 380 mm in diameter by 420 mm high withthe probe held vertically. This is comparable to the work volume ofsmall- to medium-sized CMMs which are commercially available. The ringmember 16 and the posts 14 are preferably constructed such that ring 16can be moved up and down on the posts 14, and/or that base joints 18 canbe moved to different locations around the ring member 16, to enable thesize, shape and location of the work zone or locus 32 of attainablepositions to be easily changed to accommodate particular geometries ofparts to be measured with the CMM 10. In one embodiment, the resultingstructure has nominal base lengths of 1.6 m, the minimum actuator lengthis 760 mm, the maximum actuator length is 1,295 mm, and the center rodlength is 812 mm. While use of the posts 14 and ring member 16 providecertain advantages and flexibility in use of the machine, any manner ofmounting the three base joints 18 in a fixed location can alternativelybe used.

The reference coordinate system for the machine is defined by the basejoints 18. The origin is at the center of one of the base joints 18(joint #1). The X axis lies along the line joining the centers of joints#1 and a second base joint 18 (joint #2). The Y axis is perpendicular tothe X axis and lies in the plane of the centers of the three base joint18. The Z axis is perpendicular to axes X and Y. Thus, a perfectCartesian coordinate system is unambiguously defined by the locations ofthe centers of the three base joints 18.

If the three base lengths and the absolute lengths of all six actuators18 of the hexahedron are known, then the coordinates of the centers ofthe spherical joints 26 and 28 at the top and bottom of the center pole24 are easily calculated, since each is at the apex of a tetrahedronformed by the center pole and the base sockets 18. Furthermore, theposition is unique. Any given set of lengths of the actuators 20 and 22can result in only one spatial position of the top and bottom sphericaljoints 26 and 28 on the center pole 24. Since the coordinates of thecenters of these spherical joints are known and the probe length isknown, the coordinates of the tip 64 of the probe 30 are easilycomputed. Dimensions of probed features on parts to be measured areeasily computed from the probe tip coordinate data.

The hexahedral configuration of the CMM 10 offers many advantages. Thegeometry is completely deterministic and obeys the principles of minimalconstraint and kinematic mounting. The configuration further obeys theAbbe alignment principle completely since each actuator's measurementaxis is always aligned with one of the base joints and one of the centerrod spherical joints. The design provides five degrees of freedom ofmotion (three translation, two rotation, but no rotation about the axisof the center rod). This allows the probe 30 to be oriented in anoptimal manner in relation to the surface of the work, thus reducing oreliminating errors due to directional effects in the probe 30. However,the configuration of the CMM 10 described above raises a number ofdesign challenges that have been addressed as described below. Theseinclude design of the spherical joints 18, 26 and 28, initialization todetermine the absolute lengths of the actuators 20 and 22 and distancebetween base joints 18, thermal stabilization, accurate actuator lengthmeasurement and actuation of the device 10.

FIG. 3 shows an enlarged view of one preferred embodiment of thespherical joint used in the CMM of FIG. 1. The joints use the same basicmagnetic socket and ball design as used for the LBB. In this case,however, the balls on the ends of the LBBs are replaced by magneticsockets 34. In this manner, multiple LBBs can ride on the single ball orsphere 28. While only the lower joint 28 is shown, it is understood thata similar sphere and magnetic sockets can be used for each of the basejoints and the upper spherical joint on the center pole 24. The primaryproblems with this design modification to the LBB lie in two areas. Thefirst area is interference between the sockets riding on the single ballduring machine motions. Interference can obviously be minimized bymaking the sockets 34 small in diameter relative to the ball 28.However, this strategy leads directly to the second area of concern,which is maintenance of contact between the sockets 34 and the ball 28during motion. If the socket diameter is too small, it will tip off theball rather than slide across its surface during machine motions.

The maximum allowable socket diameter can be calculated by consideringthe angle between adjacent LBB axes as the machine moves through itsworkspace. For the joint shown in FIG. 3, the minimum angle was found tobe 36° which results in a maximum allowable socket diameter of 17 mm,assuming a 50 mm diameter ball. Based on experience with the LBB, nodifficulty is encountered in fabricating magnetic sockets of thisdiameter with sufficient attractive force.

An analysis of the sliding versus tipping problem shows that this isgoverned by the coefficient of friction between the ball 28 and sockets34. The results of this analysis showed that a coefficient of frictionof less than 0.4 should result in a satisfactory performance. Themeasured coefficient of friction of the current LBB ball and socketassembly (stainless steel socket and stainless steel balls) was in theneighborhood of 0.4. Therefore, two conventional LBBs were modified byplacing small diameter sockets on their ends to test this design. It wasfound that the results confirmed the simplified analysis. Thearrangement worked satisfactorily except when the LBBs were at maximumextension which is the critical case. Here, the sockets sometimes had atendency to tip off the ball rather than slide across it. Slow andcareful motions can usually prevent this problem. However, for a robustsystem, the friction coefficient between the ball and socket can bereduced. This can be accomplished by providing anti-friction coatingsfor the surfaces of the sockets 34, including Teflon and thin-filmdiamond.

In accordance with another embodiment of the instant invention, analternative joint design, as shown in FIG. 5, is employed which uses aHooke joint (universal joint) modified to have a precision sphere 36mounted in the center thereof. The sphere 36 acts as a referenceartifact to enable detection of any deviation from true spherical motionduring operation of the joint. A Hooke joint or universal joint is aspherical joint. However, it is virtually impossible to economicallymanufacture the components of a universal joint accurately enough orstiff enough so that the assembled joint would produce truly sphericalmotion. Therefore, in accordance with the instant invention, thestationary reference sphere 36 is mounted inside the joint. Acapacitance gauge or other type of proximity gauge 66 is provided in theactuators 20 and 22 to measure the distance from the actuator end to thesurface of the precision sphere 36 as the joint articulates. In thisway, any deviations from perfectly spherical motion will be measured andcan be combined with the interferometer displacement measurements toobtain the true distance between joint centers. In an alternativeembodiment, the laser beam of the interferometer can be focused directlyonto the surface of the precision sphere 36, instead of usingretroreflectors at the ends of the actuators, thus obviating the needfor the capacitance gauges. One advantage of this alternative jointdesign is that the spheres are never touched or loaded during theoperation of the CMM 10. Therefore, wear will not be a factor and theuseful life of the joint will be increased.

FIG. 5 shows an example of the modified universal joint 38 having twooutputs 34 which is suitable for use as one of the base joints 18 on theCMM 10. The joint 38 includes a spherical four-bar linkage with twooutputs, comprised of a stationary shaft 68, a yoke 40 operable torotate about the shaft 68, three pivotable yokes 42, 44 and 46, and theprecision sphere 36 mounted on the shaft 68 at the center of the joint38. A spherical four-bar linkage with three outputs (not shown) and aprecision sphere mounted at the center point thereof can be used for thespherical joints 26 and 28 on the center pole 24, thus creating theconcentric spherical joints required by the CMM 10 of the instantinvention.

The operation of the interferometer used to determine changes in lengthof each of the actuators 20 and 22 is shown in FIG. 4. Theinterferometer includes a polarization beam splitter (PBS) 48, fixedretroreflector 50, movable retroreflector 52, optical pickup 54, andfiber optic cables 56 and 58 (only partially shown). Fiber optic cable56 transmits a light signal from a light source which, for example, maybe a suitable laser depicted by box 60. Fiber optic cable 58 transmitsthe output signal to a suitable receiver/computer depicted by box 62.Both the laser and receiver/computer are commercially available andwell-known devices.

In operation, the light beam emitted from the laser 60 is carried to thePBS by fiber optic cable 56 which is a polarization preserving cable.The laser beam is comprised of two plane and orthogonally polarizedbeams identified as lines A and B which are separated by PBS 48. PBS 48reflects the vertical component beam A to the movable retroreflector 52and the horizontal component beam B, which passes through the PBS 48, tothe fixed retroreflector 50. Beam B is relayed to the optic pick-up 54by the movable retroreflector 52 where both beams are combined andtransmitted to the receiver/computer 62. Thus, after the interferometeris energized, it is capable of ascertaining any displacement of theactuators. As the actuators 20 and 22 move relative to theinitialization point, the interferometer will register a signalindicative of a change in length of the actuator. The computer will thenperform the requisite computations to ascertain the precise changes inlength of the actuators. Inasmuch as the interferometer is only arelative displacement device, it can only measure changes in length. Inorder for the coordinates of a point to be measured, it is necessary toconvert the displacements to absolute lengths. This can be accomplishedby initializing the CMM in the manner described below, so that theinterferometer measures deviations from the initialized lengths.

In order to calculate the coordinates of the joints on the center pole24 and thereby the tip of the probe 30, the absolute distances betweenthe centers of the base sockets (base lengths), as well as the absolutelengths of the hexahedron sides, must be known. When the laserinterferometers in each actuator are turned on, the legs have somefinite length which is unknown. The interferometers keep track of thechanges in the actuator lengths as they extend and retract. However, inorder to know the absolute actuator lengths, their initial lengths atthe time the interferometers were energized must also be known. While itmight be possible to use an initialization fixture for each of theactuators, like that used for the LBB as described in the '446 patent,this would require the actuators to be removed from the machine forinitialization, which would limit the utility of the machine. Due to thephysical size of the base, it would be difficult to determine the baselengths to the required accuracy by direct measurement. Therefore, inaccordance with the instant invention, a self-initialization procedureis provided.

The hexahedral CMM 10 has only five degrees of freedom of motion, butpossesses six actuator length sensors. This implies that a redundancyexists which may be exploited to determine the initial lengths of theactuators and the base lengths. The constraint which exists is that thedistance between the centers of the top and bottom spheres on the centerrod must be constant (assuming a rigid center rod). Therefore, it ispossible to formulate the expression for the distance between the topand bottom spheres in terms of the unknown base lengths and initial leglengths plus the known leg length changes. This can be done for a numberof different positions of the center rod 24. For each position, thecenter rod length is assumed to remain constant. Thus, a least squaresproblem can be formulated to find the set of base lengths and initialleg lengths which minimize the variation in the computed center rodlength. If the center rod is designed to be stiff enough so that elasticdeformations are negligible and if the data is gathered over a shortenough period of time so that thermal changes in the base lengths andthe length of the center rod are minimized, then this procedure willresult in valid initial actuator lengths and base lengths.

The self-initialization process is used any time the power to themachine is interrupted or the laser beams are broken. Theself-initialization procedure is as follows: first, a measurement signalis obtained from the lasers in all six actuators with the center pole 24held steady. The center pole 24 is then given random smalldisplacements. These displacements should occur over a short enoughperiod of time that the center pole length and the base lengths will nothave time to undergo any thermally induced changes. After eachdisplacement, the change in the length of each actuator is determinedfrom the individual laser interferometers, as described above. When apredetermined number of such data sets have been collected, the leastsquare algorithm is used to compute the initial length of each leg, aswell as the base lengths. From this information, the spatial coordinatesof the top and bottom center rod spheres at any position of the centerrod can be computed. The spatial coordinates of the probe tip center arethen computed from knowledge of the center rod endpoints.

One of the objects of the instant invention is to produce a CMM whichneed not be housed in a specially controlled environment in order tomaintain its accuracy. However, changes in temperature will lead tochanges in the base lengths, as well as the center rod length.Therefore, in accordance with the invention, the self-initializationprocedure described above is used to continuously correct for thermallyinduced changes in the base lengths and center rod length.

During machine use, the center rod length can be calculated at eachmeasurement point as the vector distance between the top and bottomsphere centers. If, over time, this distance changes by more than someallowable tolerance, it is due to thermal growth of the base, centerpole or the unsensed portion of the leg lengths (i.e., distance from theretroreflector apexes to the ends of the legs). When this happens, theself-initialization process is repeated. In accordance with a preferredembodiment of the invention, a running buffer of information on the leglength changes is kept since initialization for the last N measurementpoints or for the last M seconds, and this information is used tocontinuously update the initialization data.

By using a continuous updating of the initialization data, the accuracyof the CMM 10 can be made insensitive to changes in its thermalenvironment. There will always be three base spheres which form a uniquecoordinate frame. The accuracy of coordinate estimation with respect tothis frame is dependent on the accuracy of knowledge of the initial leglengths and base lengths, as well as the accuracy of displacementmeasurement in each leg. The self-initialization procedure allows thebase lengths and the initial leg lengths to be continuously updated.Environmental sensors (air temperature, barometric pressure and relativehumidity) may be used in conjunction with Edlen's formula to correct forchanges in the refractive index of air, thus improving the accuracy ofinterferometric displacement measurement. As a result, the spatialcoordinate measurement accuracy of the CMM 10 is quite insensitive tothe environmental conditions, thereby reducing or eliminating the needfor environmental enclosures and allowing the machine to be useddirectly on a factory floor.

One potential area of concern is that thermal distortions of the machinebase and posts will cause changes in the location of the part withrespect to the reference coordinate frame. These deformations occur inportions of the machine which are outside of the metrology structure ofthe machine (i.e., the hexahedron) and, therefore, theself-initialization procedure will not sense these changes or correctfor them. If significant distortions of the base occur during the courseof measurement of a single object or feature, then measurement errorswill result. Conventional CMMs are also susceptible to this problem. Tohelp minimize this problem, measurements with the CMM 10 should beconducted in a short enough period of time so that such deformations arenot significant. This assumes that the spatial measurement accuracy ofthe metrology system is not adversely affected by the thermal gradients,which is not true for conventional CMMs since such gradients cause theirmembers to bend and axes to change their alignments. The spatialaccuracy of the hexahedron CMM, on the other hand, is largely unaffectedby the thermal state of the machine due to the continuousself-initialization procedure described above.

Frequent re-measurement of reference surfaces or features on the part tobe measured can be used to determine if the part is drifting withrespect to the machine coordinate system. The time constant for thermaldeformation of the machine structure connecting the part to thereference coordinate system is the determining factor for acceptablemeasurement cycle times. One design alternative to reduce this effect isto use materials with a low coefficient of thermal expansion such asInvar. However, these materials are generally considered too expensivefor general purpose CMMs. Another alternative is to increase the heatcapacity or thermal mass of the machine elements. This approachgenerally results in physically massive machine members. On conventionalCMMs, these members are a part of the kinematic structure and must moveduring the measurements. Making them massive is severely detrimental tothe dynamic performance of the machine. As an extreme example, considerthe Moore M-60 CMM (one of the most accurate of its class in the world).The maximum traverse rate for this machine is only twelve inches perminute. In contrast, on the hexahedron CMM, the material which connectsthe reference coordinate frame to the part (base plate 12 and posts 14)is not part of the kinematic structure and is intended to remainstationary. Therefore, there is no penalty in dynamic performance whenthese elements are made extremely massive and rigid.

The accuracy of displacement measurement in air using interferometry isaffected by environmentally induced changes in the refractive index oflight. For example, errors of approximately 1 part in 10⁶ will occurwith a 1° C. temperature change. Two alternatives, evacuated laser pathsand helium filled laser paths, may also be utilized to help reduce thiserror.

Since the wavelength of light is constant in a vacuum, the idealsituation for performing interferometry is to have the measurement beamtravel in a vacuum. This can be accomplished in the actuators 20 and 22by using an evacuated flexible metal bellows connecting the beamsplitter to the end of the telescoping tube. This arrangement will, ofcourse, create a force on the telescoping element, causing it to tend toretract into the cylinder. The actuation system described below mustovercome this force. Use of the evacuated bellows also allows theactuators 20 and 22 to function as pneumatic cylinders for actuation ofthe CMM. This approach to system actuation will be described more fullybelow.

Another option is to fill the inside of the actuators 20 and 22 with lowpressure helium. The refractive index of helium is approximately oneorder of magnitude less sensitive to temperature changes than air.However, if seals are used on the leg joints to prevent leakage of thehelium, it is likely that the friction of the seals would causeunacceptable hysteresis. Therefore, a cast-in-place bearing material(Moglice™) to create the sliding bearing for the movable tube can beused, resulting in acceptable frictional characteristics combined withvery small radial clearances between the shaft and bearing. A very lowsupply pressure of helium is utilized and controlled leakage is allowedthrough the small gap between the shaft and bearing. The leakage alsohelps to provide a gas cushion for the bearing, further reducingfriction.

The kinematic structure of the hexahedral CMM 10 of the invention hasbeen described in detail above. The means for actuation and control ofthis structure to produce motion of the probe tip can take a variety offorms. The structure can be treated as a passive metrology frame to beactuated manually by a human operator or by some external roboticdevice. To make maximum use of the capabilities of the hexahedron CMM10, the external motion generator must be capable of motion in the samefive degrees of freedom as the hexahedron CMM 10. Another option is tointegrate prismatic actuators into the telescoping legs or actuators 20and 22 themselves.

The preferred method is to construct the hexahedral CMM 10 as a passivedevice to be actuated externally. The University of Florida Center forIntelligent Manufacturing and Robotics GE P-60 robot has been found tobe suitable for use as an external actuation device. This six degrees offreedom manipulator is mounted adjacent to the CMM 10. The end effectorof the robot reaches into the CMM 10 workspace to grasp the center rodof the CMM 10. The robot controller is integrated with the CMM 10 toprovide position and orientation feedback of the tip of the probe 30signals during probing cycles and prevention of over-travel of any ofthe CMM legs. In this manner, the robot can be programmed to move theprobe tip through space without going outside of the CMM workspace orlocus 32, and to perform probing cycles to accomplish part measurements.

In the broadest sense of good design practice for precision machines,the instant hexahedral CMM 10 provides an advantageous configuration.The hexahedral CMM 10 serves strictly as a metrology frame and carriesnone of the actuation loads. However, the addition of an externalrobotic actuation system adds significant additional expense to themachine. Serial robots of this type are notorious for their lack ofstiffness and high mass relative to their payload capacity. These areexactly the wrong characteristics for good dynamic performance.Therefore, other methods for incorporating prismatic actuators into thelegs or actuators 20 and 22 of the CMM can be utilized. Suitablealternatives include ball screws and linear motors, as well as hydraulicand pneumatic actuators. The optical layout of the displacementmeasuring interferometer system in each leg 20 and 22 must be preservedin order to obey the Abbe alignment principle and preserve themetrological characteristics of the device. This limits the designchoices. Therefore, pneumatic actuation of the legs is typically thepreferable alternative. To preserve the integrity of the laser beamalong the axis of the leg 20 and 22, vacuum bellows can be employed toconnect the interferometer to the end of the moving tube part of theleg. Outside of this evacuated laser path, the telescoping leg 20 and 22can be constructed to resemble a double-acting pneumatic cylinder.Achievement of the required force, stiffness, speed and resolution ofactuation of a single leg enable the CMM 10 to be self-actuated. Thisembodiment will not seriously compromise the accuracy of the systemsince each of the legs 20 and 22 is loaded only in the axial directionand the actual axial length is continually being sensed by a systemwhich is largely unaffected by this load. When viewed in this sense, themetrology frame is the system of laser interferometer beams which happento be arranged coaxially within the structural elements of the CMM 10.In this manner, an improved CMM 10 is achieved which offers goodmetrology and good dynamic performance at a reasonable cost.

A preliminary error budget was constructed at the design stage of theCMM 10 of the instant invention, to determine the accuracies which werelikely to be achieved therewith. Since the hexahedron configuration ofthe CMM 10 is essentially composed of two tetrahedra sharing a commonbase, an error budget approach similar to that used for the developmentof the LBB was employed. The error budget for the LBB considered anumber of factors such as thermal and elastic growth of the unmeasuredportions of the LBB length, alignment of the beam to the sliding axisand bending of the LBB tubes, among other factors. The predictedabsolute length uncertainty was ±0.25 μm and the predicted spatialmeasurement uncertainty was ±0.6 μm. The accuracy of this instrument wassubsequently tested on the Moore M-60 CMM in Oak Ridge, Tenn. Thesetests showed a spatial measurement uncertainty of approximately ±0.5 μm,assuming the M-60 to be perfect. The agreement between experimentalresults and the error budget predictions gives confidence in theanalysis.

A similar procedure was used to estimate the uncertainty of measurementof the coordinates of the centers of the top and bottom spheres on thecenter rod 24. The probe tip location uncertainty was then obtained byprojecting lines from the extremes of the uncertainty zones for eachsphere. The result of this analysis is a projected probe locationuncertainty of ±2.8 μm. When combined with the errors induced by theprobing system, the accuracy of the CMM 10 measurements is defined. Thepreliminary error budget is shown in Table 1. This predicted accuracy isvery good for a machine of this size. More importantly, due to thedesign of the CMM 10 and the method for continuous reinitializationdisclosed above, this accuracy is essentially independent of thetemperature of the surrounding environment or the rate of change of thattemperature, thereby providing a significant improvement over knownCMMs.

As will be apparent from the description above, the instant inventionprovides applicability of platform-type mechanisms to coordinatemeasuring machines. The invention provides a novel kinematic structurewhich builds upon the inventor's previous development of the laser ballbar (LBB). This kinematic structure or hexahedral CMM 10 enablesimplementation of a continuous initialization scheme which makes theaccuracy of the CMM 10 extremely insensitive to its thermal environment.This allows the CMM 10 to be placed directly on the shop floor and morefully integrated into the production flow, thereby reducing or obviatingthe need for temperature controlled rooms and significantly reducinginstallation costs for CMMs. In addition, the CMM 10 of the instantinvention has significantly better dynamic performance, because the massof the moving elements therein is much lower than in conventional CMMdesigns.

While the preferred forms and embodiments of the invention have beenillustrated and described, it will be apparent to those of ordinaryskill in the art that various changes and modifications may be madewithout deviating from the inventive concepts and spirit of theinvention as set forth above, and it is intended by the appended claimsto define all such concepts which come within the full scope and truespirit of the invention.

                  TABLE 1                                                         ______________________________________                                        Hexahedral CMM - Preliminary Error Budget                                     Error Source           (-) μm                                                                             (+) μm                                      ______________________________________                                        Thermal Growth Between Spheres and Optics                                                            -0.3200 0.3200                                         Cosine Alignment of Laser to Slide Motion                                                            -0.0584 0.0000                                         Sphere-line Misaligninent to Slide Motion                                                              0.0000                                                                              0.0866                                         Deadpath               -0.3127 0.3127                                         Beam Misalignment from Optic's Rotation                                                              -0.2251 0.0000                                         Sphericity of Ball/Socket Combination                                                                -0.1200 0.1200                                         Elastic Elongation of Components                                                                     -0.0094 0.0000                                         Laser Stability and Intrinsic Factors                                         Laser Stability        -0.0160 0.0160                                         Polarization and Incidence Alignment                                                                 -0.0008 0.0008                                         Fiber Optic Cable Mechanical Errors                                                                  -0.0400 0.0400                                         Fiber Optic Cable Thermal Errors                                                                     -0.1900 0.1900                                         RSS LENGTH ERROR       -0.5538 0.5099                                         Mean RSS LENGTH ERROR  -0.5319 0.5319                                         Error in Position of Probe Tip                                                X                      -1.5649 1.5649                                         Y                      -1.4338 1.4338                                         Z                      -1.9000 1.9000                                         PROPAGATED ERROR OF PROBE TIP                                                                        -2.8486 2.8486                                         ______________________________________                                    

I claim:
 1. A coordinate measuring device, comprising three sphericalbase joints, means for maintaining said base joints in a fixed spacedrelation, six actuator assemblies each having a variable length, whereineach of said base joints has a first end of two of said six actuatorassemblies connected therewith, respectively, a center pole having afirst spherical joint connected to a first end thereof and a secondspherical joint connected to a second end thereof, wherein a second endof a first one of each of said two actuator assemblies connected to eachof said base joints is connected to said first spherical joint of saidcenter pole and a second end of a second one of each of said twoactuator assemblies connected to each of said base joints is connectedto said second spherical joint of said center pole in a manner whichforms a hexahedron, said device further including a probe mounted at oneend of said center pole and means for determining a change in length ofeach of said six actuator assemblies upon movement of said probe.
 2. Acoordinate measuring device as defined in claim 1, wherein said meansfor determining a change in length of each of said six actuatorsincludes a laser interferometer.
 3. A coordinate measuring device asdefined in claim 2, wherein each of said six actuator assemblies has ahollow interior and said means for determining a change in length ofeach of said six actuators further includes means for delivering a laserbeam to said hollow interior of each of said actuator assemblies.
 4. Acoordinate measuring device as defined in claim 3, wherein said meansfor delivering said laser beam includes single mode, polarizationpreserving, fiber-optic cable.
 5. A coordinate measuring device asdefined in claim 1, wherein said base joints are spheres, and said firstends of said actuator assemblies are magnetic sockets which enableconnection with said spheres by a magnetic force.
 6. A coordinatemeasuring device as defined in claim 1, wherein said first and secondspherical joints on said center pole are spheres, and said second endsof said actuator assemblies are magnetic sockets which enable connectionwith said spheres by a magnetic force.
 7. A coordinate measuring deviceas defined in claim 1, wherein said base joints and said first andsecond spherical joints are spheres, and said first and second ends ofsaid actuator assemblies are magnetic sockets which enable connectionwith said spheres by a magnetic force.
 8. A coordinate measuring deviceas defined in claim 1, wherein said base joints are universal joints. 9.A coordinate measuring device as defined in claim 1, wherein said firstand second spherical joints on said center pole are universal joints.10. A coordinate measuring device as defined in claim 1, wherein saidbase joints and said first and second spherical joints are universaljoints.
 11. A coordinate measuring device as defined in claim 10,wherein said universal joints each include a stationary reference spheremounted at a center point thereof, and said device further includesmeans for using said reference sphere to enable compensation for anynon-spherical motion by said universal joints during movement of saidprobe.
 12. A coordinate measuring device as defined in claim 11, whereinsaid means for using said reference sphere includes a proximity gaugewhich measures a distance between said actuator assemblies and saidreference sphere, respectively, during movement of said probe.
 13. Acoordinate measuring device as defined in claim 11, wherein said meansfor using said reference sphere includes means for enabling said laserbeam to reflect off of said reference sphere.
 14. A coordinate measuringdevice as defined in claim 1, wherein said means for maintaining saidbase joints in a fixed spaced relation includes a support leg for eachbase joint.
 15. A coordinate measuring device as defined in claim 1,wherein said means for maintaining said base joints in a fixed spacedrelation includes a ring member and means for supporting said ringmember, and further wherein said ring member includes means for enablingsaid base joints to be selectively connected with said ring member at aplurality of different relative positions thereon to enable modificationof a locus of attainable positions of said probe.
 16. A coordinatemeasuring device as defined in claim 1, further comprising means forself-initializing said device, including means for displacing saidcenter pole a plurality of times, means for obtaining information on achange in the length of each of said actuator assemblies for eachdisplacement, and means for using said information and a least squarealgorithm to determine an initial length of each leg and a distancebetween each of said base joints, thereby enabling initialization ofsaid device.
 17. A coordinate measuring device as defined in claim 16,wherein said means for displacing is operable to displace said centerpole said plurality of times at a rate which is more than the rate atwhich the device is capable of undergoing any significant thermallyinduced changes.
 18. A coordinate measuring device as defined in claim16, further including means for continuously performing saidself-initialization procedure during operation of said machine to enableaccuracy of said device to be insensitive to changes in environmentalconditions.
 19. A method of initializing a coordinate measuring machine,said machine including three spherical base joints, means formaintaining said base joints in a fixed spaced relation, six actuatorassemblies each having a variable length, wherein each of said basejoints has a first end of two of said six actuator assemblies connectedtherewith, respectively, a center pole having a first spherical jointconnected to a first end thereof and a second spherical joint connectedto a second end thereof, wherein a second end of a first one of each ofsaid two actuator assemblies connected to each of said base joints isconnected to said first spherical joint of said center pole and a secondend of a second one of each of said two actuator assemblies connected toeach of said base joints is connected to said second spherical joint ofsaid center pole in a manner which forms a hexahedron, said devicefurther including a probe mounted at one end of said center pole andmeans for determining a change in length of each of said six actuatorassemblies upon movement of said probe,said method comprising the stepsof displacing said center pole a plurality of times, obtaininginformation on a change in the length of each of said actuatorassemblies for each displacement, and using said information and a leastsquare algorithm to determine an initial length of each leg and adistance between each of said base joints.
 20. A method of initializinga coordinate measuring machine as defined in claim 19, further includingthe step of continuously performing said self-initialization procedureduring operation of said machine to enable accuracy of said device to beinsensitive to changes in environmental conditions.